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By their calculations, the Mercator projection scores 8.296 and Winkel Tripel does better at 4.563. Their own azimuthal equidistant double-sided projection, meanwhile, scores 0.881.
Map the region’s boundary using the azimuthal equidistant projection, initially guessing where the geographic center might be, and centering the map there.
“For example, Mercators projection is true to scale only along the equator, and azimuthal projection is limited to convergence of the meridians at one pole at a time.